A novel lever-type elastic metamaterial model for low-frequency wave attenuation

Design and numerical validation of quasi-zero-stiffness metamaterials for very low-frequency band gaps

In this paper, inerter-based dynamic vibration absorbers (IDVAs) are applied in elastic metamaterials to broaden low-frequency band gaps. A discrete mass-spring lattice system and a distributed metamaterial beam carrying a periodic array of IDVAs are, respectively, considered. The IDVA consists of a spring and an inerter connected to a traditional mass-spring resonator. Compared to the traditional resonators, the special designed IDVAs generate two local-resonance (LR) band gaps for the discrete lattice system, a narrow low-frequency band gap and a wider high-frequency one. For the distributed IDVA-based metamaterial beam, in addition to the generated two separated LR band gaps, the Bragg band gap can also be significantly broadened and the three band gaps are very close to each other. Being able to amplify inertia, the IDVAs can be relatively light even operated for opening up low-frequency band gaps. When further introducing a dissipative damping mechanism into the IDVA-based metamaterials, the two close-split LR band gaps in the lattice system are merged into one wide band gap. As for the metamaterial beam with the dissipative IDVAs, an even wider band gap can be acquired due to the overlap of the adjacent LR and Bragg-scattering band gaps.

Elastic metamaterials possess band gaps, or frequency ranges that are forbidden to wave propagation. Existing solutions for impeding three-dimensional (3D) wave propagation largely rest on high-volume fractions of mass inclusions that induce and tailor negative effective density-based local resonances. This study introduces a class of elastic metamaterials that achieve low-frequency band gaps with a volume fraction as low as 3% (mass density as low as $0.034\phantom{\rule{0.1em}{0ex}}\mathrm{g}/{\mathrm{cm}}^{3}$). The working of the proposed design hinges on a 3D trampolinelike mode behavior that gives rise to wide, omnidirectional, and low-frequency band gaps for elastic waves despite very low-mass densities. Such a 3D trampoline effect is derived from a network of overhanging nodal microarchitectures that act as locally resonating elements, which give rise to band gaps at low frequencies. The dynamic effective properties of the metamaterial are numerically examined, which reveal that the band gap associated with the trampoline effect is resulted from a negative effective modulus coupled with a near-zero yet positive effective density. The experimental characterization is then made possible by fabricating the metamaterial via a light-based printing system that is capable of realizing microarchitectures with overhanging microfeatures. This design strategy could be useful to applications where simultaneous light weight and vibration control is desired.

A novel one-dimensional quasi-zero-stiffness (QZS) metamaterial is proposed in this paper to acquire low-frequency band gaps to control the low-frequency longitudinal vibration of propulsion shaft using the bionic QZS as the local resonant oscillator. Firstly, the parameter design of the representative unit cell (RUC) for metamaterials using a bionic limb-shaped QZS structure is carried out and static analysis is conducted to verify its QZS property. Secondly, we model the QZS metamaterials as a lumped-mass-spring chain and derive the dispersion relationship through the Harmonic Balance method, then discuss the impact of damping, stiffness ratio, mass ratio, and excitation amplitude on this band gap. Finally, the resulting band gap is then confirmed through numerical simulations. Both the theoretical and numerical predictions show very low-frequency band gaps (about 7.5 Hz). Therefore, the proposed QZS metamaterials should be a promising solution for low-frequency wave filtering or attenuation for longitudinal vibration of ship shafting.

This paper presents the modeling technique, design method, a new working mechanism and influence factors for elastic metamaterials (EMs) with parallel multi-resonators for broadband elastic vibration suppression. The general formula of the effective mass is deduced, and the effects of the relevant structural parameters on the frequency regions of the negative effective mass are illustrated in details. Subsequently, the dispersion relation and transmission spectrum of the EMs are studied. Based on the theoretical approach, the EMs plates were proposed, and the formation mechanism of the band gaps are analyzed by studying the displacement field of the eigenmodes at the band gaps edges. The related results well confirm that the novel EMs induces multi-frequency negative effective mass, and the number of the regions is equal to the number of the local resonators. The start frequencies of the band gaps are decided by the natural frequencies of each resonator, and the width of frequency band with negative effective mass can be broadened by enlarging the mass ratio of the local resonator. The EMs plate with the thickness of only 2.5 mm designed on the basis of theoretical research exhibits two flexural vibration band gaps (FVBGs) with the total width of 78.4 Hz below 200 Hz, which has been verified by the transmission testing experiments. For the formation mechanism of the FVBGs, the vibration is localized in the according resonator at the lower edge of each band gap, while at the upper edges the local resonance mass and the base plate vibrate in a reverse phase. Based on the theoretical and numerical analyses, the EMs with multiple parallel local resonators would be used in various fields, such as noise and vibration isolation, filters, and other renewed devices.

A numerical simulation study on elastic wave propagation of a phononic composite structure consisting of epoxy and tungsten carbide is presented for low-frequency elastic wave attenuation applications. The calculated dispersion curves of the epoxy/tungsten carbide composite show that the propagation of elastic waves is prohibited inside the periodic structure over a frequency range. To achieve a wide bandgap, the elastic composite structure can be optimized by changing its dimensions and arrangement, including size, number, and rotation angle of square inclusions. The simulation results show that increasing the number of inclusions and the filling fraction of the unit cell significantly broaden the phononic bandgap compared to other geometric tunings. Additionally, a nonmonotonic relationship between the bandwidth and filling fraction of the composite was found, and this relationship results from spacing among inclusions and inclusion sizes causing different effects on Bragg scatterings and localized resonances of elastic waves. Moreover, the calculated transmission spectra of the epoxy/tungsten carbide composite structure verify its low-frequency bandgap behavior.

The mitigation of a planar shock wave caused by a cloud of calibrated water droplets was studied both experimentally and numerically. Experiments were carried out, with different shock wave Mach numbers ranging from 1.1 to 1.8, in a vertical shock tube coupled with a droplet generator which produced a well-characterized cloud of droplets of 120, 250 and 500 μm in diameter. By exploiting such an experimental set-up, we successfully measured the attenuation of a normal shock wave when passing through the water droplet cloud. This series of experiments allowed to identify the main parameters of this investigation and a clear dependence between the attenuation of the shock wave and terms governing the regimes of droplet breakup has been found. On the other hand, to support this experimental approach, 1D unsteady calculations were performed in similar configurations. Although the mathematical model based on an Eulerian/Eulerian approach was actually incomplete, the first comparisons between the experiments and the simulations were rather interesting and pointed out the need to improve the physical model, by taking into account the fragmentation and the vaporization of the droplets submitted to the shock wave as well as the size distribution of the water spray.

In the framework of multiple-scattering theory, we show that the dispersion\nrelations of certain electromagnetic (EM) and elastic metamaterials can be\nobtained analytically in the long-wavelength limit. Specific examples are given\nto the two-dimensional metamaterials with cylindrical inclusions arranged in\nsquare and triangular lattices. The role played by the lattice structure in\ndetermining whether a dispersion relation is isotropic or not is shown\nexplicitly. Different lattice dependences between EM and elastic metamaterials\nare also shown. In the case of isotropic dispersions, our results coincide with\nthose of isotropic effective medium theories obtained previously for EM and\nelastic metamaterials, respectively, and, therefore, provide a more fundamental\nsupport to those theories. In the case of elastic metamaterials with\nanisotropic dispersions, our analytical results can provide an anisotropic\neffective medium theory in the form of Christoffel's equation. In this case,\nthe isotropic effective medium theory can describe accurately the\nangle-averaged dispersion relations. The properties of anisotropic dispersions\nare discussed and verified by numerical calculations of a realistic elastic\nmetamaterial.\n

Elastic and acoustic metamaterials are man-made structures designed to control and manipulate waves through band gaps. The generalized bandwidth of metamaterials with locally resonant (LR) band gaps is usually narrow, limiting their applications in noise and vibration control. On the other hand, nonlinear metamaterials with dipolar resonances can present a broad chaotic band with low amplitude resonances due to bridging coupling, which is only observed under sufficiently large excitation amplitudes. In this work, we show that bridging-coupling phenomenon can also be observed in linear metamaterials with dipolar resonance, producing a special pass band with low amplitude resonances at low frequencies without excitation amplitude dependence. Such phenomenon emerges in a modified resonant metachain with zigzag interconnections and is based on the isomerism of traditional metamaterials. Although this modified isomer preserves the static stiffness and mass density (i.e., static performance) of the original metamaterial, its dispersive behavior presents interesting properties (i.e., branches with negative mass features and overlapping of opposite group velocity), resulting in an overall negative effective mass between the LR band gaps that is responsible for the remote interaction and the enhanced wave performance. In addition to the theoretical discussions, the bridging coupling is experimentally observed in a three-dimensional printed elastic metamaterial rod supporting longitudinal waves. The design can be extended to elastic bending, acoustic and electromechanical media, as well as to systems with periodicity in two and three dimensions (i.e., plates and solids). Therefore, the findings of this work open avenues to investigate the bridging-coupling phenomenon in linear systems as well as to explore the properties of metamaterial isomers.

Mechanisms of multi-bandgap inertial amplification applied in metamaterial sandwich plates

Widely tunable magnetorheological metamaterials with nonlinear amplification mechanism

The attenuation of planar shock waves generated by plate impact was monitored by their decay throughout massive nickel blocks. This was accomplished, during the passage of the wave, by manganin piezoresistive gages connected to oscilloscopes and, in the post-shocked condition, by hardness measurements and TEM observations at various distances from the impact surface in the nickel blocks. The nickel systems exhibited different metallurgical microstructures before shock loading: preshocked (grain size 150 μm), annealed (grain size 150 μm)and annealed (grain size 32 μm). For each system two different initial shock pressures were used: 10 and 25 GPa. The pulse duration was held constant at 2 μs. The experimental records of oscilloscopes showed that there are no significant effects of grain size and pre-deformation on the attenuation in nickel. The observed attenuation was compared with the calculated one according to hydrodynamic theory and poor agreement was found, An “accumulation” model based on the conservation of energy is presented herein to explain the dissipative processes of shock waves in metals.

The development of engineering technology puts forward more demanding requirements for the performance of materials, many of which cannot be met by the existing natural materials. In addition to exploring and refining new natural materials, it is possible to arrange designed microstructures according to periodicity or other rules to produce man-made materials that do not exist in nature itself, mostly due to the development of additive manufacturing (AM) technology. These artificial materials are known as metamaterials. In the past few years, the design and application of metamaterials have made great progress. This paper reviews the research of elastic metamaterials in recent years, which includes both traditional metamaterials with fixed structural properties and active metamaterials with tunable properties. Among many application scenarios, this paper mainly focuses on elastic metamaterials’ applications in vibration control, impact mitigation and wave attenuation. In addition, this paper also discusses the development of metamaterial inverse design or optimization design, with special attention to the application of topology optimization (TO) technology in this area.

Presented in this paper are study results of dispersion relationships of periodic structures composited of concrete and rubber, from which the frequency band gap can be found. Two models with fixed or free boundary conditions are proposed to approximate the bound frequencies of the first band gap. Studies are conducted to investigate the low-frequency and directional frequency band gaps for their application to engineering. The study finds that civil engineering structures can be designed to block harmful waves, such as earthquake disturbance.

In order to achieve the attenuation of low‐frequency sound, in this paper, a hybrid metamaterial structure with a complete band gap below 500 Hz is proposed, which is subjected to second‐order fractal, series fusion, and whether the structure is framed or not to form 8 different structures. Based on the finite element method and Bloch's theorem, the bandgap and transport properties of all model structures are evaluated, and the bandgap and propagation properties of metamaterial structures with different fractal levels are elucidated in terms of band structure and group velocity. In addition, the third‐order fractal structure and the dependence of the band gap on the material are also studied. The results show that the structure has a superior band gap width, and the complete band gap of its tandem fusion structure accounts for up to 45.502% in the range of 500 Hz, and the second‐order fractal has a complete band gap of 45.588% in the range of 1000 Hz. Compared with other structures, it can produce lower and better band gap. The research in this paper provides a new strategy for realizing acoustic metamaterial structures with low frequency band gaps.